I've done analog design for many years and I'm not aware of much available for doing the initial design approach. It really depends upon the knowledge and experience of the designer. Certainly, at a minimum you need a basic knowledge in all things electronic: electric and magnetic fields, DC and AC circuit theory (resistors, capacitors, inductors, transformers), semiconductor theory (diodes, transistors, SCRs, triacs, etc.), amplifier design (transistor, op amps, etc.). Without that basic knowledge, it would be difficult to sythesize an otimum analog design given a set of requirements.
From the basic knowledge of how various circuit elements work, you work to generate a circuit that will do what you want. In general you try to come up with more than one approach and then pick the one that is the most simple but still meets all the requirements. As part of this effort you would likely simiulate parts of the circuit with SPICE to verify that it works as desired. At the end, of course, you would want to simulate the complete circuit (or as much as possible, based upon its complexity). Finally, you breadboard the circuit to verify it's operation. Of course, if you're referring the design of the actual IC chip then it may not be possible to breadboard since the complexity of the circuit and/or the effect of parasitics will make a breadboard impractical.
For a beginner it's a great help to have a mentor with experience in the area you're working but I know that's not always possible. A good place to start is a Google search for design information about a particular problem you're trying to solve. And forums like this, of course, are a good source of information. But, in general, analog design synthesis is a creative process that, at least at the present state of computer tools, is still largely done by the human brain. There are few short cuts.